Question

On a recent trip to the convenience store, you picked up 3 gallons of milk, 4 bottles of water, and 7 snack-size bags of

chips. Your total bill (before tax) was $23.40. If a bottle of water costs twice as much as a bag of chips, and a gallon of
milk costs $2.20 more than a bottle of water, how much does each item cost?

Answer 1

bottle of water: $1.60

gallon of milk: $3.80

bag of chips: $0.80

Explanation:

First, the amount of groceries bought can be represented as:

`3m + 4w + 7c = \$ 23.40`

where
`m` represents the cost of one gallon of milk,
`w` represents the cost of a bottle of water,
`c` represents the cost of one bag of chips.

We can form a system of equation by constructing another equation to substitute into the first using the other pieces of information given.

"a bottle of water costs twice as much as a bag of chips"

`w = 2c` →
`c = (w)/(2)`

"milk costs $2.20 more than a bottle of water"

`m = w + \$ 2.20`

Now, substitute these into the first equation and solve for w in terms of c.

`3(w + 2.20) + 4w + 7\cdot (w)/(2) = 23.40`

`3w + 6.60 + 4w + (7)/(2) \, w = 23.40`

`(21)/(2) \, w = 16.80`

`21w = 33.60`

`w = 1.60`

So, one bottle of water costs $1.60.

To solve for the other items, plug the solved value into the 2-variable equations.

`m = 1.60 + 2.20`

`m = 3.80`

So, one gallon of milk costs $3.80.

`c = (1.60)/(2)`

`c = 0.80`

So, one bag of chips costs $0.80.